Researches on granular reasoning based on granular space

Based on the method of mixing logical reasoning with granules, an extended reasoning, called granular reasoning, is introduced, which proceeds within the formulas defined in this paper, and is determined by operations of granules. The analyses indicate that granular reasoning includes the reasoning in rough logic. The researches show that granular reasoning is an extension of the reasoning in classical logic. Thus, granular reasoning not only establishes a theoretical foundation for rough logic, but also set up a new method of logical reasoning. Since granular reasoning is closely connected with granular computing, and is different from other researches that scholars made on granular computing by logical ways, granular reasoning must starts a new channel, and will develops a certain circumstances for the further investigations on granular computing.